Well, I'm not a journalist any more! I work in finance now, though I do lots of interviews with media (largely the business press).
All of what you say is I think correct, big picture. And I don't know for sure the cause. But . . .
The single most important event in US journalistic history over the last 50 years was the Washington Post's exposure of Watergate. The NYT, LA Times and Time magazine -- among others -- deserve credit too, and when Walter Cronkite at CBS blessed the story by featuring it prominently later during the investigation (and he was certainly not perceived as liberal, nor was CBS), he elevated it, followed by the coverage of the Watergate hearings live. It took TV to turn the tide of US sentiment against Nixon, but it was the Post that did the first digging, and the heavy lifting.
Bob Woodward (who was a Republican but didn't vote for Nixon), Carl Bernstein (an unabashed counter-culture liberal), editor Ben Bradlee (a friend of JFK and a Democrat) and Katherine Graham (the owner of the Post, and an upper crust conservative who was friends with a number of government officials in the Nixon White House) -- all became folk heroes -- especially Woodward and Bernstein, and especially after All the President's Men, which was about the journalistic process as much as the story itself.
But because the Nixon administration painted the Post as a tool of the hysterical left -- much as Trump has done the MSM -- and because the Post were vindicated, and clearly were instrumental in bringing down the presidency -- print journalism in America I think became a field that left-leaning change agents flocked to over a long time. It was a place where you could be a hero or heroine. We should add the break in values during the 60s and 70s over Vietnam too (largely a TV story) -- again an example of exposing the American public to the realities of a modern war supported by conservative doctrine which helped spark new liberalism, and made TV its tool (or vice versa maybe).
I have some other thoughts on the British press mission being to protect the glory days of England's English-ness, which is a conservative trope, but they are half-baked.